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  <div class="section" id="numpy-correlate">
<h1>numpy.correlate<a class="headerlink" href="#numpy-correlate" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.correlate">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">correlate</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">v</em>, <em class="sig-param">mode='valid'</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/numpy/numpy/blob/v1.18.1/numpy/core/numeric.py#L647-L713"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#numpy.correlate" title="Permalink to this definition">¶</a></dt>
<dd><p>Cross-correlation of two 1-dimensional sequences.</p>
<p>This function computes the correlation as generally defined in signal
processing texts:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">c_</span><span class="p">{</span><span class="n">av</span><span class="p">}[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">sum_n</span> <span class="n">a</span><span class="p">[</span><span class="n">n</span><span class="o">+</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">conj</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="n">n</span><span class="p">])</span>
</pre></div>
</div>
<p>with a and v sequences being zero-padded where necessary and conj being
the conjugate.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>a, v</strong><span class="classifier">array_like</span></dt><dd><p>Input sequences.</p>
</dd>
<dt><strong>mode</strong><span class="classifier">{‘valid’, ‘same’, ‘full’}, optional</span></dt><dd><p>Refer to the <a class="reference internal" href="numpy.convolve.html#numpy.convolve" title="numpy.convolve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">convolve</span></code></a> docstring.  Note that the default
is ‘valid’, unlike <a class="reference internal" href="numpy.convolve.html#numpy.convolve" title="numpy.convolve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">convolve</span></code></a>, which uses ‘full’.</p>
</dd>
<dt><strong>old_behavior</strong><span class="classifier">bool</span></dt><dd><p><em class="xref py py-obj">old_behavior</em> was removed in NumPy 1.10. If you need the old
behavior, use <em class="xref py py-obj">multiarray.correlate</em>.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray</span></dt><dd><p>Discrete cross-correlation of <em class="xref py py-obj">a</em> and <em class="xref py py-obj">v</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.convolve.html#numpy.convolve" title="numpy.convolve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">convolve</span></code></a></dt><dd><p>Discrete, linear convolution of two one-dimensional sequences.</p>
</dd>
<dt><code class="xref py py-obj docutils literal notranslate"><span class="pre">multiarray.correlate</span></code></dt><dd><p>Old, no conjugate, version of correlate.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The definition of correlation above is not unique and sometimes correlation
may be defined differently. Another common definition is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">c</span><span class="s1">&#39;_</span><span class="si">{av}</span><span class="s1">[k] = sum_n a[n] conj(v[n+k])</span>
</pre></div>
</div>
<p>which is related to <code class="docutils literal notranslate"><span class="pre">c_{av}[k]</span></code> by <code class="docutils literal notranslate"><span class="pre">c'_{av}[k]</span> <span class="pre">=</span> <span class="pre">c_{av}[-k]</span></code>.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">correlate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">])</span>
<span class="go">array([3.5])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">correlate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="s2">&quot;same&quot;</span><span class="p">)</span>
<span class="go">array([2. ,  3.5,  3. ])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">correlate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="s2">&quot;full&quot;</span><span class="p">)</span>
<span class="go">array([0.5,  2. ,  3.5,  3. ,  0. ])</span>
</pre></div>
</div>
<p>Using complex sequences:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">correlate</span><span class="p">([</span><span class="mi">1</span><span class="o">+</span><span class="mi">1</span><span class="n">j</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="o">-</span><span class="mi">1</span><span class="n">j</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="n">j</span><span class="p">],</span> <span class="s1">&#39;full&#39;</span><span class="p">)</span>
<span class="go">array([ 0.5-0.5j,  1.0+0.j ,  1.5-1.5j,  3.0-1.j ,  0.0+0.j ])</span>
</pre></div>
</div>
<p>Note that you get the time reversed, complex conjugated result
when the two input sequences change places, i.e.,
<code class="docutils literal notranslate"><span class="pre">c_{va}[k]</span> <span class="pre">=</span> <span class="pre">c^{*}_{av}[-k]</span></code>:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">correlate</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.5</span><span class="n">j</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="o">+</span><span class="mi">1</span><span class="n">j</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="o">-</span><span class="mi">1</span><span class="n">j</span><span class="p">],</span> <span class="s1">&#39;full&#39;</span><span class="p">)</span>
<span class="go">array([ 0.0+0.j ,  3.0+1.j ,  1.5+1.5j,  1.0+0.j ,  0.5+0.5j])</span>
</pre></div>
</div>
</dd></dl>

</div>


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